Newton’s & Coulombs Laws in Light of the Small Atomic Nucleus

Newton’s & Coulombs Laws in Light of the Small Atomic Nucleus AAPT Meeting Spring 2007 Rose-Hulman J.O. Brooks, Ivy Tech

Topics Requiring Acceptance • 1. Electric and Gravitational Fields in atom are comparably nearly equal. • 2. A radial solution to Schrödinger’s equation exists, (Needed for Unified Field) • 3. There is a Unified Field. • 4. Macroscopic Quantum Gravity is well defined. • 5. Therefore: General Relativity is applicable to atomic phenomena.

Electric and Gravitational Fields are nearly equal. • Dirac: • Reality • Answer: Employ Newton’s These are Forces Question: Can one use 1836 as the central mass of the hydrogen atom ??? 1

Possibly In Your First Contact with Newton’s Law You Saw - - And you were informed that the value of k is one when the unit kilogram is used

The Universal Constant G Really has Only One Mass Unit in It This is the k Kg with k = 1 and K remains 1 when the unit (em) is used

Because K is Unity it has Multiple Facets Given the Central Mass unit, the k value is one of that Unit

very The Alternative is not Attractive Implication is 1 Kg 1.7 x 10-27 Kg Wouldn’t the Nucleus prefer to orbit the electron

Notice that the Value of R is Inherently Composite in G because of Kepler’s Law Kepler’s Law has no unit of Mass but the unit of mass in G requires a unit k………………..k is the unit of orbiting mass

There is a radial solution to Schrödinger’s equation 2

Explanation of my Radial Solution of Schrödinger’s Equation, R in Å • A d’Alembertian in Cylindrical Coordinates This is a format of one wave equation developed by d’Alembert & Euler in 1760 from a consideration of the Lagrangian.

Unified Field is Inherent in the Bohr’s Derivation of Rydberg’s Constant 3 BUT time The Radical is Unity Divide both Sides by unit mass squared and the resultant expression has the units of G, Newton’s Universal Gravitational Constant

Conventional orbit Mismatch One Circumferential orbit in time traverses 4 Radii Conclusion: Never a Mismatch

Forming Fields from Rydberg’s Equation G = Units Certainly Agree Rydberg Version of the Unified Field We can now add relative permittivity which when identified with the Poisson accomplishes the equality.

The Rydberg Constant as Derived by Bohr can be Related to Newton’s G How we were rid of that pesky coulomb It was necessary to divide by the unit kilogram squared to achieve the units equivalent to G

Expediency of the Use Electron Masses was Established Applies to the entire table To Complete the Field a Radial solution is Needed I derived this radial solution in the nineteen sixties  Is set equal to unity

Calculation of Rydberg Series’ Radii Setting N = 40.54189 for hydrogen gives R = .529 Å for n = 1. The radial values shown are iterated for f thus finding R for n = 1, 2, 3 … Above Values for n= 1,2 ….10 are Plotted in the Next Slide on Radial Distribution

Setting Up Aufbau Matrices for any Atom of the Table • s p d f • N • N+5 N+6 • N+10 N+11 N+12 • N+15 N+16 N+17 • N+20 etc. N, the Principle Attribute, is Periodic with Atomic Number

Spreadsheet Formulation  Radius Å Radius MKS Absolute Frequency = 9 N2 -271 N + 588 Sum Shell Radii

Associated Matrix Formulas Using Parametric Equations of Radius The Poisson

The Real Index Called the Attribute Compared to the Integral Quantum Number n Base frequency is fixed by N and outer orbital frequencies are iterated to conform to spectra

DistinguishThree Cases from Bohr’s Rydberg Derivation The Atomic Case without Radii A Next B C

Based on TheirVelocities Planet Perihelion Mean Aphelion 4

.Show: The sun has a charge of 1.9 x 1038 Charge to mass ratio of the sun is (-) 9.8 x 107 Planets charge to mass ratio is (+) 7.7 x 1029 Planets test charge to mass ratio (-)9.4 x 107

Electro-Magnetic Gravitation Planet

Radii are a Solution to Schrödinger’s Equation in Cylindrical Coordinates The Poisson has the same form of the Polynomial form of a wave equation derived by d’Alembert and Euler in 1700’s from a consideration of the Lagrangian – Encyclopedia Mathematiics

Electron Mass of Unified g in Unit Test Mass of 1 em This is applicable to any Atom at any orbital provided the underlying orbital is taken as a point and the radius in question is to be added to the previous radius

Example: Boron N ValuesAlpha Values Radii per electron per orbital Radii of entire orbital

√c√Rg √Rg 4  2cV/h From Spectra

Newton’s & Coulombs Laws in Light of the Small Atomic Nucleus